Question

Consider the function: f(x) = 0.5x if 0<x<1 f(x) = 0.5 if 1<x<2 f(x) =1.5-0.5x if...

Consider the function:

f(x) = 0.5x if 0<x<1

f(x) = 0.5 if 1<x<2

f(x) =1.5-0.5x if 2<x<3

f(x) = 0 otherwise.

a. Show that this is a PDF.

b. Calculate P(x<2.5) and P(0.5<x<2).

c. Find the expected value and the median of this distribution.

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose X is a random variable with pdf f(x)= {c(1-x) 0<x<1 {0 otherwise where c >...
Suppose X is a random variable with pdf f(x)= {c(1-x) 0<x<1 {0 otherwise where c > 0. (a) Find c. (b) Find the cdf F (). (c) Find the 50th percentile (the median) for the distribution. (d) Find the general formula for F^-1 (p), the 100pth percentile of the distribution when 0 < p < 1.
Let X be the random variable with probability density function f(x) = 0.5x for 0 ≤...
Let X be the random variable with probability density function f(x) = 0.5x for 0 ≤ x  ≤ 2 and zero otherwise. Find the mean and standard deviation of the random variable X.
7. For the random variable x with probability density function: f(x) = {1/2 if 0 <...
7. For the random variable x with probability density function: f(x) = {1/2 if 0 < x< 1, x − 1 if 1 ≤ x < 2} a. (4 points) Find the CDF function. b. (3 points) Find p(x < 1.5). c. (3 points) Find P(X<0.5 or X>1.5)
6. A continuous random variable X has probability density function f(x) = 0 if x< 0...
6. A continuous random variable X has probability density function f(x) = 0 if x< 0 x/4 if 0 < or = x< 2 1/2 if 2 < or = x< 3 0 if x> or = 3 (a) Find P(X<1) (b) Find P(X<2.5) (c) Find the cumulative distribution function F(x) = P(X< or = x). Be sure to define the function for all real numbers x. (Hint: The cdf will involve four pieces, depending on an interval/range for x....
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and...
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and 0 otherwise (a) Find the value c such that f(x) is indeed a density function. (b) Write out the cumulative distribution function of X. (c) P(1 < X < 3) =? (d) Write out the mean and variance of X. (e) Let Y be another continuous random variable such that  when 0 < X < 2, and 0 otherwise. Calculate the mean of Y.
Suppose X, Y, and Z are random variables with the joint density function f(x, y, z)...
Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z ≥ 0, and f(x, y, z) = 0 otherwise. (a) Find the value of the constant C. (b) Find P(X ≤ 0.75 , Y ≤ 0.5). (Round answer to five decimal places). (c) Find P(X ≤ 0.75 , Y ≤ 0.5 , Z ≤ 1). (Round answer to six decimal...
1. Suppose a random variable X has a probability density function f(x)= {cx^2 -1<x<1, {0 otherwise...
1. Suppose a random variable X has a probability density function f(x)= {cx^2 -1<x<1, {0 otherwise where c > 0. (a) Determine c. (b) Find the cdf F (). (c) Compute P (-0.5 < X < 0.75). (d) Compute P (|X| > 0.25). (e) Compute P (X > 0.75 | X > 0). (f) Compute P (|X| > 0.75| |X| > 0.5).
Let f(x) = e^-2(2^x)/x! for x= 1,2,3,... and 0 otherwise. Show that f(x) is a pdf....
Let f(x) = e^-2(2^x)/x! for x= 1,2,3,... and 0 otherwise. Show that f(x) is a pdf. Find the expected value of f(x).
f '(−3) = f '(−2) = f '(0) =  f '(1) = 0, f '(x) < 0...
f '(−3) = f '(−2) = f '(0) =  f '(1) = 0, f '(x) < 0 if x < −3 or −2 < x < 0 or  x > 1 f '(x) > 0 if −3 < x < −2 or 0 < x < 1 f ''(x) < 0 if −2.5 < x < −1 or x > 0.5 f ''(x) > 0 if x < −2.5 or −1 < x < 0.5 Sketch the graph of a function
Consider the following the density function: f(x) = 2(1 – x) 0 < x < 1...
Consider the following the density function: f(x) = 2(1 – x) 0 < x < 1 0 elsewhere a. What is the expected value of X? b. What is the variance of X? c. What is F(x), the CDF of X.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT